Some remarks on singular solutions of nonlinear elliptic equations. III: viscosity solutions, including parabolic operators

TL;DR

This paper investigates singular solutions of nonlinear elliptic equations, focusing on viscosity solutions, and extends classical principles like the Hopf Lemma and maximum principle to include parabolic equations.

Contribution

It advances the theory of viscosity solutions by strengthening classical results and extending them to parabolic operators, addressing singularities and boundary behavior.

Findings

Removable singularities for viscosity solutions identified

Strengthened Hopf Lemma including parabolic equations

Established maximum principle for viscosity solutions with parabolic operators

Abstract

The paper concerns singular solutions of nonlinear elliptic equations, which include removable singularities for viscosity solutions, a strengthening of the Hopf Lemma including parabolic equations, Strong maximum principle and Hopf Lemma for viscosity solutions including also parabolic equations.